Use Of Dynamic Geometry Software Research Articles

The quality of prospective mathematics teachers' dynamic geometry tasks in terms of the coordination between mathematical depth levels and technological actions

AbstractBackgroundTeachers must have the skills to find, select, design and use technology‐based mathematical activities that focus on high‐level cognitive demands—supporting student reasoning. However, they experience various difficulties in creating, planning and making decisions about how and when to utilize technological affordances.ObjectivesThis study aims to examine the quality of prospective school mathematics teachers' (PMTs) tasks containing the use of dynamic geometry software through the analysis of the coordination between mathematical depth levels (MDLs) and technological actions (TAs), according to Trocki and Hollebrands', Digital Experiences in Mathematics Education, 2018, 4, 110–138, Dynamic Geometry Task Analysis Framework.MethodsWithin groups, PMTs designed lesson plans that included dynamic geometry tasks (DGTs) based on the learning outcomes of the middle school mathematics curriculum. They then created micro‐teachings of these tasks. The participants' DGTs and transcripts of their microteaching videos were the main data sources.ResultsWe found that many prompts included no TA or a single TA, regardless of the prompts' MDLs. Moreover, the results showed that the high‐depth prompts aimed to contribute to students' reasoning processes on geometric concepts through the TAs, which required specific tools such as dragging and sliding to get generalizations. Although the groups differed in the quality and number of DGTs, the groups' lesson plans mostly contained low‐ or medium‐quality DGTs regarding the coordination between MDLs and TAs.ConclusionsInforming PMTs about high‐quality technology tasks and increasing their awareness on this matter is a priority to encourage them to incorporate innovative technological activities in their mathematics instruction.

The Use of Dynamic Geometry Software in Mathematics Education Research

Bu araştırmada; Matematik Eğitimi araştırmalarında Dinamik Geometri Yazılımlarının kullanımına yönelik alan yazında yer alan araştırmaları incelemek amaçlanmıştır. Bu amaçla araştırmada Türkiye’de matematik eğitimi alanında yapılmış yüksek lisans ve doktora tezleri ile ulusal hakemli dergilerde yayınlanan makaleler incelenerek, kriterlere uygun 209 çalışma detaylı bir şekilde taranıp betimsel analizi yapılmıştır. İlgili araştırmalara ulaşabilmek için; dinamik yazılım, dinamik geometri, dinamik geometri yazılımı ile Geogebra ve Cabri, Geometer’s Sketchpad anahtar kelimeleri çerçevesinde tarama yapılmıştır. Araştırmanın bulguları yıllar, anahtar kelimeler, örneklem sınıf düzeyleri, örneklem büyüklükleri, kullanılan yöntemler, kullanılan dinamik yazılım, desenleri/modelleri, veri toplama süreçleri ile veri toplama araçları ve analiz yöntemleri şeklinde temalara ayrılmıştır. Veriler, kodlama ve frekansa dayalı olarak MS Excel programı ile belirlenerek yorumlanmış, bulgular tablolarla ve grafiklerle sunulmuştur. Elde edilen bulgulara dayanarak, yapılan araştırmaların yöntem olarak çoğunluğunda nitel araştırma yöntemlerinden betimsel analiz kullanıldığı; verilerin ise en çok başarı testleri aracılığıyla elde edildiği tespit edilmiştir.

Matematik Öğretmenlerinin Dinamik Geometri Yazılımı Temelli Acil Uzaktan Öğretim Sürecine Özgü Orkestrasyon Tiplerinin İncelenmesi

The aim of this study is to examine secondary school mathematics teachers’ orchestration types specific to their dynamic geometry software-based emergency remote teaching. The theoretical lens of the study is instrumental orchestration in which teachers’ teaching styles with the use of technological tools are defined as orchestration types. The study was designed as a case study whose participants were two secondary school mathematics teachers (Faruk and Ela) experienced in the use of dynamic geometry software in their face-to-face teaching processes. Semi-structured interviews and observations were performed in order to collect the data in the study. The collected data were analyzed through qualitative content analysis method. The results of the study reveal that the teachers developed two new orchestration types during the emergency remote teaching process While Faruk developed the Teacher-in-sherpa-role orchestration in which the teacher performed the operations asked by the students; both teachers performed the Screen-as-board in which they used virtual pen to draw auxiliary lines, place marks and take notes on the screen. In addition, Ela adapted the Monitor-and-guide orchestration into her teaching process, in which a student-monitoring system regarding dynamic geometry activities played an essential role. The results show that various orchestration types identified in the literature do not occur in the remote teaching processes due to their characteristics regarding the physical classroom environment. It is suggested that further studies focus to examine the orchestration types developed by mathematics teachers in the post-pandemic remote teaching processes.

Acceptance and Intentions of Using Dynamic Geometry Software by Pre-Service Primary School Teachers

In this paper, we empirically verify the validity of the extended Technology Acceptance Model (TAM) for the use of Dynamic Geometry Software (DGS) in teaching geometry, as proposed by Pittalis. The model includes the notion of “perceived pedagogical-learning fit” in addition to the traditional belief and attitude variables of TAM. We employ a structural equation modeling approach to capture the relationships between the different latent constructs. With a sample of 135 pre-service primary school teachers as participants, our study provides valuable insights into the factors influencing the adoption of DGS in geometry teaching. The results reveal that the extended TAM serves as a suitable framework to evaluate the intentions of teachers to use DGS in teaching geometry. However, we also observe some discrepancies in the predictive power of various latent factors when compared to the original study. These findings not only contribute to our understanding of the factors affecting the adoption of DGS in geometry teaching but also provide valuable insights for future research and practice.

An interdisciplinary educational path to understand the economic phenomena of a fluid and complex world with mathematics

In this paper, we describe an activity that involves economics and mathematics. It is included in the planning of orientation paths towards university studies within the Mathematical High School Project and is dedicated to students in the last years of high school. In particular, this research will deal with the issue of solving an economic problem using not only real analysis instruments but also geometrical topics concerning Euclidean geometry and topology. Mathematics becomes a language to understand and explain a real life problem, such as determining the optimal position of an airport, a nuclear reactor and so on. Some activities made use of dynamic geometry software and computer simulations.

Mathematics Teachers’ Geometric Thinking: A Case Study of In-service Teachers’ Constructing, Conjecturing, and Exploring with Dynamic Geometry Software

<p style="text-align:justify">Many research studies have been conducted on students’ or pre-service teachers’ geometric thinking, but there is a lack of studies investigating in-service teachers’ geometric thinking. This paper presents a case study of two high school teachers who attended the dynamic geometry (DG) professional development project for three years. The project focused on the effective use of dynamic geometry software to improve students’ geometry learning. The two teachers were interviewed using a task-based interview protocol about the relationship between two triangles. The interviews, including the teachers' work, were videotaped, transcribed, and analyzed based on the three levels of geometric thinking: recognition, analysis, and deduction. We found that the participating teachers manifested their geometric skills and thinking in constructing, exploring, and conjecturing in the DG environment. The study suggests that the DG environment provides an effective platform for examining teachers' geometric skills, and levels of geometric thinking and encourages inductive explorations and deductive skill development.</p>

Connections Between Prospective Middle-Grades Mathematics Teachers’ Technology-Enhanced Specialized Content Knowledge and Beliefs

The authors explore the influence of instructional technologies on teachers’ subject-matter knowledge as well as how this knowledge is mediated by context, experience, and beliefs about teaching, mathematics, and technology. This study examined how four pre-service middle grades mathematics teachers’ (PSTs) beliefs about teaching, mathematics, and technology influenced their subject matter knowledge specific to the teaching profession (i.e, specialized content knowledge [SCK]). Embedded-unit single case study analysis revealed that PSTs’ different beliefs about teaching, mathematics, and technology indicated various impacts of the use of dynamic geometry software on their SCK. PSTs who viewed teaching mathematics with technology as an effective pedagogical decision to support students’ understanding and self-discovery of their subject matter knowledge demonstrated more dynamic SCK with dynamic geometry software. The authors discuss interconnections between PSTs’ beliefs and knowledge and share implications for technology-enhanced teacher education of middle grades mathematics teachers.

Developing students' problem posing skills with dynamic geometry software and active learning framework

In the present study, the effects of using dynamic geometry software in active learning framework on students’ problem posing skills and their views about problem posing were examined. The participants consisted of 16 eighth-grade students. Data were collected by problem posing tests, open-ended questions, student diaries, and dynamic geometry software supported tasks. The study, designed with the embedded mixed method, lasted 13 weeks. The dependent t-test was used in the analysis of quantitative data, and descriptive analysis was performed in qualitative data. Problem posing skills of students examined according to use of mathematical language, grammar and expression, suitability to acquisitions, quantity and quality of data, solvability, originality, solution of the problem criteria. In the present study, it was determined that the use of dynamic geometry software in active learning framework developed students’ problem posing skills. The problems that students posed in the dynamic geometry software during the implementation process indicated improvement in terms of problem posing skills as the weeks passed. It was found that students had positive views about the problem posing process, while they experienced some difficulties in this process.

The mathematical and technological nature of tasks containing the use of dynamic geometry software in middle and secondary school mathematics textbooks

The mathematical and technological nature of tasks containing the use of dynamic geometry software in middle and secondary school mathematics textbooks

Instrumentation Schemes for Solving Systems of Linear Equations with Dynamic Geometry Software

In this paper we focus on the link between the use of dynamic geometry software and student understanding for the solution of systems of linear equations from an instrumental genesis perspective. Three task-based interviews were conducted with an undergraduate linear algebra student majoring in mathematics education and proficient in using dynamic geometry software. Data included video recordings, student written work and screen recordings. The data analysis was guided by the theoretical lens of instrumental genesis, to elaborate on how student thinking was shaped by the use of the digital artefacts. The digital technology supported the participant’s solution steps and over time the student developed four interrelated instrumentation schemes, which are parameter scheme, combined algebra and geometry scheme, the intersection of figures scheme and echelon form scheme.

The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: A Meta-Analysis Study

The purpose of this study was to (1) assess the impact of using Dynamic Geometry Software (DGS) on students’ mathematical abilities, (2) determine the differences in effectiveness based on study characteristics in order to help educators decide under what conditions the use of DGS would be suitable in improving students' mathematical abilities. This meta-analysis study investigates 57 effect sizes from 50 articles that have been published in journals, international and domestic proceedings from 2010 to 2020 using the Comprehensive Meta-Analysis (CMA) tool as a calculation tool. Meanwhile, the Hedges coefficient is applied to the calculation of the effect size at the 95% confidence level. Based on a random effect model with a standard error of 0.09, the analysis results have found an overall effect size of 1.07. This means that learning using DGS has a high positive effect on students' mathematical abilities. The effect size of 1.07 explains the average student who uses DGS exceeds 84% math ability of those in conventional classes that are initially equivalent. Analysis of the study characteristics found significant differences in terms of sample size, student to computer ratio, and education level. This research showed the DGS used was more effective under certain conditions. First, it is very effective in sample conditions less than or equal to 30. Second, it provides classrooms with a sufficient number of computers, allowing students to use them individually, which is required to achieve higher effectiveness levels. Third, DGS is effective in high schools and colleges than in junior high schools. These facts can help educators in deciding on the appropriate sample sizes, student to computer ratios, and future levels of education in using DGS.

AS PESQUISAS SOBRE O USO DE SOFTWARES DE GEOMETRIA DINÂMICA NO BRASIL

Este trabalho é um recorte de uma pesquisa realizada no Programa de Pós-Graduação em Educação em Ciências e Matemática da Universidade Federal de Goiás (UFG). Foram realizados o mapeamento e a análise das pesquisas publicadas entre 1987 e 2017, que abordam o ensino de geometria plana no ensino médio com o uso de softwares de geometria dinâmica como recurso didático. Para tanto, os procedimentos metodológicos do Estado do Conhecimento nos guiaram no planejamento, na organização, análise e apresentação dos dados encontrados. O campo empírico baseou-se nos bancos de dados das bibliotecas de instituições que possuem mestrado e doutorado relacionados à Educação Matemática e no Banco de Teses e Dissertações (BDTD) da CAPES. Definiu-se como marco inicial o ano de 1987, por ser o ano de criação do 1º software de geometria dinâmica e 2017 como marco final devido ao de que o levantamento foi realizado em 2018. Os resultados indicam o Geogebra como o software mais utilizado nas experiências com o ambiente dinâmico. Outro aspecto que emerge dos dados coletados são influências da teoria dos registros de representação semiótica e da didática francesa. As perspectivas são permeadas por uma discussão que valoriza o “aprender a aprender” e a formação para o mercado de trabalho, focando nos aspectos técnicos em detrimento da construção de conceitos geométricos.

Teachers\u2019 Involvement in Designing MERLO Items: Boundary Crossing

Meaning Equivalence Reusable Learning Objects (MERLO) items are a new kind of didactical tool that can be designed by teachers and used in classes, in tasks aimed at engaging students in deep reasoning, exploring and arguing about mathematical concepts. The interactions across communities of mathematics teachers and educators in on-line professional development were studied with attention to the phenomenon of boundary crossing of MERLO items, viewed as boundary objects in this article. The study analyseda first (international) crossing of the object that passedinstitutional boundaries (between Australian and Italian school systems), and a second crossing of the same object –inside the Australian institutional community – that passed boundaries (from static to dynamic representations) that we interpret in terms of method both for teachers and for researchers. This passage is possible due to the use of dynamic geometry software (GeoGebra) that supported a modification in the design of the item. The analysis shows boundary crossing as a process of transformation that can influence a modification (more or less stable) in the practices of the teachers involved and provides a deep research insight in relation to existing theoretical frameworks.

GeoGebra for learning and teaching: A parallel investigation

In the study reported on here, we investigated the effects of the use of dynamic geometry software (DGS) (i.e., GeoGebra) on learners’ learning and a teacher’s beliefs. The learners and teacher involved in the study were from a high-poverty, rural high school in South Africa. We compared grade 11 learners (N = 56) who used GeoGebra in the context of learning circle geometry with learners who experienced geometry through traditional lecture-based instruction. Participating learners were from classes in a public school located in the rural Umkhanyakude district of KwaZulu-Natal, Republic of South Africa. Results showed that learners using GeoGebra were more successful at solving problems and justifying their statements, while the other learners provided a limited justification for their answers. In a parallel and complementary investigation the teacher’s attitudes toward using GeoGebra as an instructional tool were considered qualitatively. Results showed that even in high-poverty, rural settings where the availability of technological resources are limited, the use of GeoGebra affected learners’ learning and had positive effects on the teacher’s beliefs regarding teaching and learning. Keywords: Euclidean geometry; GeoGebra; performance; theorems and proofs

Aktivitas Guru Matematika dalam Pembelajaran Menggunakan Perangkat Lunak Geometri Dinamis

This study aims to describe the use of dynamic geometry software (DGS) by mathematics teachers in their teaching and learning activities. This study case involves two junior high school mathematics teachers who use DGS in their teaching activities. The data of this study were collected by recording teacher activity and interviewing the teachers. The data were then analyzed through data transcription, data categorization, data reduction, data review and analysis, and conclusion. The results of this study involved, first, the use of DGS in teaching and learning activities can be categorized into two activities: 1) shifting and 2) delivering content. The delivering content is later divided into two activities: a) applying representation and b) modeling. Shifting activity occurred when teachers had an interval period while conducting one activity to another. Delivering content-applying representation activity occurred when teachers were using DGS to deliver both conceptual and procedural materials to the students. Delivering content-modeling activity occurred when teachers were using DGS to make students acquire knowledge and have a problem-solving skill as performed by their teachers. The modeling activities occurred either explicitly and implicitly.

The Use of Dynamic Geometry Software from a Pedagogical Perspective: Current Status and Future Prospects

This research firstly aims to reveal the pedagogical potentials and limitations of dynamic geometry software (DGS). For this purpose, research on Cabri (2D/3D/Plus), the Geometer’s Sketchpad, GoogleSketchUp, GeoGebra and Logo software was reviewed and compiled. As a result of the research, it appears that DGS offers an effective pedagogical environment because of its ability to interact with digital materials and allow for geometric objects to be seen from all sides. However, we found that teachers have some problems in combining DGS with class pedagogy. In this study, the effects of gender, age, education level, skill in using technology and the influence of professional experience were also examined in relation to primary school mathematics teachers’ preferences in using DGS. As a result of this research, it was found that GeoGebra and Cabri were the most-used DGS packages by primary school mathematics teachers, while other geometry software was less preferred by teachers.

Transformations and Buried Treasure

The treasure hunt takes my classroom to the world and features a variety of approaches, conjecture building, and the use of dynamic geometry software. The problem has been written about extensively (Gamow 1947; Nahin 2016; Shilgalis 1998; Shriki 2011). Here is the problem as I have adapted it for my students.

A Case Study of Two Selected Teachers as they Integrated Dynamic Geometry Software as a Visualisation Tool in Teaching Geometry

This paper reports on an aspect of a larger research study conceptualised within a teacher development project in Mthatha, Eastern Cape Province. The project was initiated with the objective to develop appropriate skills to use dynamic geometry software (DGS) effectively and strategically as a teaching and learning tool for mathematics. The study reported in this paper aims specifically to ascertain how selected mathematics teachers integrated co-developed technologically aided visualisation tools in the observed lessons. The case study involved two teachers from different schools. The data sources were the classroom observations followed by stimulated reflective interviews with the teachers. The data were analysed to study the use of DGS visualisation tools in relation to Kilpatrick’s framework of teaching proficiency. The lessons evidenced a displayed alignment with the elements of teaching proficiency in the context of teaching geometry. The dynamic visualisation opportunities offered by DGS proved to supplement the teaching repertoire for the participating teachers. Pedagogical practices influence the use of DGS, as evident from the lessons when the participating teachers incorporated collaboratively developed GeoGebra applets into their classrooms. We argue that the collaborative engagement between teachers appears to be a positive way forward in closing the gap between having access to technology and adapting it for effective use in mathematics classrooms.

Exploring Properties of Quadrilaterals in the Poincaré Disk Model of Hyperbolic Geometry Using the Dynamic Geometry Software

The purpose of this study was to have preservice mathematics teachers explore important properties of hyperbolic quadrilaterals in the Poincaré disk model using the Dynamic Geometry Software (DGS). The participants comprised 40 preservice mathematics teachers at Rajabhat Rajanagarindra University, Thailand, who had enrolled in the Foundations of Geometry course at the second semester of the academic year 2015. The instruments were activity packages exploring properties of hyperbolic quadrilaterals using DGS. The results indicated that preservice mathematics teachers could make conjectures and verify properties of hyperbolic quadrilaterals correctly and rapidly. The use of DGS can help students visualize this abstract geometry.

Mathematical modelling with digital tools—a quantitative study on mathematising with dynamic geometry software

The use of digital tools in mathematics lessons has recently gained in significance, especially because of ongoing technical developments. Particularly in the context of mathematical modelling, digital tools have become more and more important. They have been deployed for many years and are currently being intensively discussed from a didactical point of view. This paper discusses to what extent modelling processes using digital tools can be described theoretically, and surveys significant empirical findings in this field. Based on a quantitative control study with 709 students, we especially investigated the competence of mathematising. We compared the competence development of a test-group that worked with digital tools, to a control-group that worked with paper and pencil on the same tasks during a four-lesson intervention on geometric modelling tasks. We find a comparable improvement of mathematising in both groups. This competence development was also investigated in relation to the influence of attitudes towards the software used and program-related self-efficacy. We find program-related self-efficacy, but not attitudes towards the used software, to be a significant predictor of the gain in competency. These results are discussed with respect to different performance studies examining the use of dynamic geometry software.